Implementing OAuth within my game itself

For that particular game engine you would need to consult with their support or community, but if it works with a website, then you can implement a normal web oAuth login at an ‘account’ website you put up for your game, have your users login via there, and then check their login validity from within your game by connecting to internet.

There are other topics which revolve around the same concept - you can get some logic examples from them: